- #1
BucketOfFish
- 60
- 1
Suppose I have a set that contains all sets that it does not contain. Obviously no such set exists because the thing I just said makes no sense. I might as well say consider the natural number which is greater than zero and less than one. No such thing exists. So I don't understand why Russell's Paradox isn't just considered wordplay too - it defines a set that doesn't make sense, so obviously that set doesn't exist. It's like a self-contained reductio ad absurdum.
Now, here's another way of looking at things, which is sort of facetious. Say you have a shelf in a library that is just filled with indexes. Some of those indexes list themselves (for whatever reason). If you wanted to, you could make an index which lists every other index that does not list itself, and then you could either add the index to its own list or choose to leave it out. The index is then an actual existing object which contains the things it contains, regardless of how you choose to describe it. You could talk about a hypothetical index which lists every index that does not list itself, but that's just talk, because no such thing exists or could exist, and the fact that you could talk about such a thing does not undermine the existence or consistency of your shelf full of indexes in any way.
Now, here's another way of looking at things, which is sort of facetious. Say you have a shelf in a library that is just filled with indexes. Some of those indexes list themselves (for whatever reason). If you wanted to, you could make an index which lists every other index that does not list itself, and then you could either add the index to its own list or choose to leave it out. The index is then an actual existing object which contains the things it contains, regardless of how you choose to describe it. You could talk about a hypothetical index which lists every index that does not list itself, but that's just talk, because no such thing exists or could exist, and the fact that you could talk about such a thing does not undermine the existence or consistency of your shelf full of indexes in any way.